SIMULTANEOUS IONOSPHERIC VARIABILITY ON EARTH
AND MARS
Michael Mendillo1, Steven Smith1, Joei Wroten1, Henry Rishbeth1,2, and David Hinson3
1
Center for Space Physics
Boston University
Boston, MA 02215
2
Department of Physics and Astronomy
University of Southampton
Southampton SO17 1BJ, UK
3
Department of Electrical Engineering
Stanford University
Stanford, CA 94305-9515
ABSTRACT
Ionospheric physics deals with the basic structure and variability of plasma within the upper
atmospheres of the Earth and planets. Comparative studies foster both exploration and synthesis
within diverse settings. In this paper, we examine observations of the ionospheric profiles on
Mars obtained on 9-27 March 1999 by the radio science experiment onboard the Mars Global
Surveyor satellite, and compare their day-to-day variability with same-day observations on
Earth. Using photochemical-equilibrium arguments applicable to the peak electron density layer
on Mars and the E-layer on Earth, we find basic agreement in scaling laws between the planets,
and in the details of correlations with simultaneous solar flux variations during a period of
pronounced solar activity. We ascribe the residual variabilities (larger on Mars than Earth) to
both observational uncertainties and to non-solar mechanisms in need of further study on both
planets.
1. INTRODUCTION.
1.1. Comparative Ionospheres.
The ionized component of a planet’s upper atmosphere depends on a blend of in-situ production
and loss processes, plus effects of transport of ionization into or out of the local region of
interest. As described in basic texts on ionospheric physics (Ratcliffe, 1960; Davies, 1969;
Rishbeth and Garriott, 1969; Bauer, 1973; Banks and Kockarts, 1973; Kelley, 1989; Hargreaves,
1992; Schunk and Nagy, 2000), each of these processes enjoys a mature level of understanding.
Computer models of the terrestrial ionosphere are plentiful (Schunk, 1996, 2002) and each
ionosphere in our solar system has at least one model (Nagy and Cravens, 2002).
JGR (final revised copy – 12 August 2003)
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The truly common input for all solar system ionospheres on a given day is the Sun’s photon flux,
a simple function of heliospheric distance. All other effects are planet specific:
(a) rotation rate and solar obliquity conditions,
(b) the thermal structure, constituent reactions, and dynamics of its neutral atmosphere,
(c) the degree to which energetic particles (of solar wind and/or magnetospheric origin) impinge
upon its atmosphere,
(d) diffusion and electrodynamics associated with coupling from above, and
(e) tides, waves, and electrodynamics arising from coupling to regions below.
Given the variety of possible ionospheres in our solar system that might result from these
variable processes, it is not obvious, a priori, which of the planets would have the greatest
electron density. One approach to a solar-system-wide assessment is to focus on the dominance
of the in-situ mechanisms: production by solar radiation and chemical loss. Fortunately, as we
shall see, there are ionospheric layers on each planet for which plasma dynamics is either
unimportant, or its importance occurs at heights well above the regions of peak solar production
and dominant chemical loss. In the next section, we review briefly the photochemical basis of
such ionospheric regions, and then apply the results to known ionospheres over a span of 30
astronomical units (AU) in the solar system.
1.2. Photochemical Ionospheres.
Ionospheric physics at each planet involves a local blend of two fundamental regimes:
photochemical processes and neutral/plasma dynamics. On Earth, where photochemical
processes are reasonably well understood, dynamical effects related to upward and downward
coupling are used to explain the departures often observed from the predictions of simple
photochemistry. Such attempts for other planets are far less constrained because of the lack of
comprehensive measurements of ionospheric parameters. In this section, we review briefly the
most general formulation of a photochemical ionospheric layer in order to explore its
ramifications as a base level description of ionospheres throughout the solar system. We
conclude the section with a discussion of how simplifying assumptions employed in such a
formulation affect scaling laws for ionospheric behavior among the planets.
If all planetary atmospheres had (a) a single molecular gas that is photoionized to form a
molecular ion, (b) for which dissociative recombination is the dominant loss process, (c) located
in a dense atmosphere, making transport negligible, and (d) with no magnetospheric or solar
wind interaction (or considering latitudes and altitudes where they are small), then simple
photochemical equilibrium would govern each planet’s peak electron density. Under such
conditions, the daytime electron (and ion) density N is never far from the steady state value
derived from “Chapman theory” (Chapman, 1931, Rishbeth and Garriott, 1969, Bauer, 1973). In
this situation, the rate of loss αN2 (where α is the recombination coefficient) balances the rate of
production P, i.e.,
P = αN2
(1)
2
where
P = n(M) η σ S e-τ / D2
(2)
Here, D represents heliocentric distance in AU, S the photon flux of solar ionizing radiation
outside the atmosphere at 1 AU, τ the optical depth for the ionizing radiation, n(M) the molecular
number density, σ the cross-section for absorption of the ionizing radiation, and η the “ionization
efficiency” (number of electrons produced per photon absorbed).
For a single ionizable gas M, the optical depth τ at any point is given by an integral along the
path between that point and the Sun. For an exponential atmosphere with scale height H, at solar
zenith angle χ, the integration results in the equation
τ = n(M) σ H sec χ
(3)
Practical observations are often concerned with the maximum electron density Nm of an
ionospheric layer. The peak of a photochemical (“Chapman”) layer lies near the level of unit
optical depth (τ = 1). Imposing the condition τ = 1 in (2) and (3) gives the equation for the peak
production rate at the height of the peak, hm (where e = 2.718…):
Pm = S η cos χ /e H D2
(4)
This expression is independent of both n(M) and σ, which through equation (3) determine the
height hm at which the peak forms, but not the peak density. Equating (1) and (4) yields the result
that the maximum ionospheric electron densities scale inversely with distance from the Sun:
Nm = [S η cos χ /e H α]1/2 / D
(5)
For Earth, the classic example of this process is the formation of O2+ from O2. In other planetary
cases, the molecular ion produced by photoionization of the dominant neutral species (e.g., CO2+
for Mars and Venus, and H2+ for jovian planets) can react very rapidly with ambient neutrals to
form a different molecular ion (e.g., O2+ and H3+). The terrestrial analogy is the rapid
transformation of N2+ to NO+. For our purposes, this simply means that photoproduction leads to
a dominant daytime molecular ion – not necessarily the ion that is originally formed – on time
scales faster than any possible plasma dynamics. This assumption – that the photochemical
situation is not materially altered by charge-exchange or other reactions (such as attachment of
electrons to form negative ions), so that the plasma exists as molecular ions and electrons – is
central to our analysis. There are, however, other provisos associated with these equations:
(a) Because η, σ and S are all wavelength dependent, integration over the whole ionizing
waveband, and summation over all ionizable gases, is needed to evaluate P properly. For present
purposes, we may continue to use the simple equations if we consider η and σ to be appropriately
weighted averages, and S the total ionizing flux.
(b) The appropriate numerical value of the flux S at 1 AU differs between planets, because the
wavelength range of the ionizing radiation depends on the ionizable gas.
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(c) Similarly, the cross-section σ and the ionization efficiency η depend on the gas being ionized
at each planet.
(d) The scale height H depends not only on the mass of the ionizable gas, but also on the
temperature in each planetary atmosphere and the planet’s gravity.
(e) If H varies with height, an extension of Chapman theory (Nicolet, 1951) shows that the
exponent of cos χ in equations (4) and (5) is modified from 1 to (1+dH/dh), which for the
terrestrial E-layer is about 1.5. Chapman theory can be further extended to take account of
grazing incidence (i.e., χ approaching 90o). For present purposes we do not incorporate these
refinements.
(f) The dissociative recombination coefficient α depends on the reactants present and on their
temperatures and vibrational states.
Keeping to these assumptions, and returning to equation (3), another useful relation emerges, one
based on the fact that the product of neutral gas concentration n and neutral scale height H is
proportional to column content. Thus, for overhead Sun (χ = 0), an ionospheric peak occurs at
the same column content on any planet (and, through the hydrostatic equation, to pressure).
These statements, too, are subject to proviso (c) about the cross-section σ, and to others:
(g) If the loss coefficient α or the scale height H are height-varying, the level of peak production
may not coincide with the level of maximum electron density (In practice, the difference
between them is only a fraction of a scale height).
(h) The relation between optical depth and pressure depends on molecular mass and gravity,
which vary from planet to planet.
With concerns (a) through (h) all duly noted, there is still utility in saying sunlight is sunlight and
molecules in an atmosphere are similar, and thus proceed with equation (5) as an initial
framework for comparative ionospheric scaling.
1.3. Observations of Ionospheres in the Solar System.
The most recent summary of planetary ionosphere appears in Nagy and Cravens (2002). We
refer the reader to that work and references therein for a planet-by-planet account of the
dominant photochemical processes responsible for the main ionospheric layer at each planet. As
also pointed out in Nagy and Cravens (2002), Venus has the most completely observed extraterrestrial ionosphere, with the four jovian planets having only a few profiles available from
satellite “fly-by” encounters, and these yield far from consistent descriptions. In Figure 1 we
offer an attempt to summarize the diverse measurements of peak electron densities for the seven
planets with substantial atmospheres in our solar system. In virtually all of the non-terrestrial
cases, the measurements are not at the sub-solar point, nor at the same levels of solar activity.
Thus, uncertainty ranges spanning diurnal, seasonal and solar cycle values are also indicated for
the three terrestrial planets, and for Jupiter and Saturn (estimates that probably apply to Uranus
and Neptune as well).
Clearly there is not an overall 1/D pattern as equation (5) would suggest: the peak density does
not occur on the innermost planet, but on the third one (depicted by the open triangle symbol at
the 1 AU position). The reason is again photochemical in origin: the conditions leading up to
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equation (5) do not hold for the Earth’s F2-layer, where the maximum electron density occurs.
Atomic oxygen (O) is the main ionizable gas in the F-region and the resulting O+ ions cannot
recombine with electrons via dissociative recombination, thus violating both the fundamental
photochemical assumptions that lead to equation (5). Electrons in the terrestrial F2 layer are lost
by a slow two-stage process involving reactions with neutral N2 and O2, and thus the rate of
electron loss at the peak is of the form βNm rather than αNm2 (Rishbeth and Garriott, 1969).
Finally, plasma transport is highly significant for the F2-layer, a factor not included in equations
(1) to (5). For all of these reasons, the F2-layer’s peak electron density (NmF2) is not the
appropriate parameter to represent the Earth in Figure 1, where all other planets have their peak
densities in a pure photochemical layer.
The terrestrial ionosphere has photochemically controlled electron density layers below the peak
layer, as do several of the planets. The E-layer at 100-120 km is produced by EUV of about 9001000 Ǻ and X-rays, and the F1-layer at 170-200 km is produced by shorter EUV (roughly 200900 Ǻ). These two layers are the ones most consistent with the assumptions leading to equation
(5). For reasons discussed more fully below (dealing with F1-layer departures from pure
photochemical equilibrium), we select the terrestrial E-layer for appropriate comparisons with
Mars and thus add a typical value of its peak density (NmE) at the 1 AU position in Figure 1.
With this single change, the pattern of Nm~1/D is clearly more apparent for all the solid triangle
symbols (denoting photochemical layers) in Figure 1. Indeed, a least squares fit to the seven
solid triangle points in Figure 1 gives an empirical scaling result consistent with the dependence
shown in equation (5). While this trend spans the solar system, sub-trends seem to exist for the
terrestrial planets and for the jovian planets when taken separately. These sub-trends are related
to the parameters taken to be first-order constants in equation (5) when, in fact, they can vary.
Yet, as discussed above, there are only two main molecular ions (O2+ and H3+) found among the
seven photochemically dominant peak layers in the solar system, thus accounting for the
consistent picture suggested by Figure 1.
1.4. Approach to Earth-Mars Comparative Ionospheric Studies.
The goal of this paper is to conduct the first detailed comparative study of two solar-controlled
ionospheres, terrestrial and martian, to test the scaling laws with distance and day-to-day solar
variability embodied in equation (5). Bougher et al. (1999, 2002) have provided comprehensive
summaries of the upper atmospheres of the terrestrial planets, and we will draw from those
studies for the discussions below. As will be seen, there are two ionospheric layers on Mars and
two on Earth that could form the bases of a comparative study of photochemical ionospheres.
For Mars, the maximum electron density occurs near 135 km where the pressure is ~ 5 × 10-7
mbar and the dominant ion is O2+. Photons below ~900 Å (and primarily at 304 Å) provide the
ionization source of CO2, and rapid chemistry converts CO2+ to O2+ (Nagy and Cravens, 2002).
A secondary ledge of molecular ions and electrons occurs near 110 km (10-5 mbar), produced
primarily by soft X-rays (18-150 Å) (see Bougher et al., 2001 and references therein).
Understanding the main ionospheric layer at 135 km on Mars is clearly the best starting point for
comparative studies: it is more readily (and reliably) observed, and the solar wavelengths
responsible for its production conform more directly to those responsible for the terrestrial E and
F1 layers.
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For Earth, the E-layer plasma (e-, O2+, N2+, NO+) is well represented by the physics embodied in
equation (5). It occurs at ~110 km where the pressure level is ~8 × 10-5 mbar. The F1 layer is
typically at ~ 3 × 10-6 mbar and thus, from our discussion of optical depth, column content and
pressure in section 1.2, it might appear to be the better layer for comparative studies with the
peak layer on Mars. Yet, the F1-layer (which is more of a “ledge” than a “layer”) is primarily
formed by the ionization of atomic oxygen (O), a process of minor importance on Mars. In
addition, only some of the terrestrial O+ ions are subsequently converted to molecular ions.
Thus, the F1-layer is a transition region between the predominance of atomic and molecular ions,
and consequently the electron loss processes involve a blend of the βNm and αNm2 regimes
mentioned above. The associated time constants for loss range from seconds to tens of minutes
(e.g., as shown in Banks and Kockarts (1973)), indicating that dynamics start to become
important as the F1 layer merges into the F2 layer. Observationally, the F1 peak density is often
difficult to identify unambiguously in ionograms, and thus attempts to characterize its day-to-day
variability are fraught with uncertainty. An excellent summary of E region observations and
modeling using the most recent reaction rates and atmospheric parameters has been given by
Titheridge (2000), with the problem of E-F1 layer transition physics and detection explored in
Titheridge (2003).
Based on the above discussion, i.e., for reasons both physical and practical, we will adopt the
purely photochemical terrestrial E-layer as the appropriate one for observational comparisons
with the maximum electron density on Mars. Embodied in this decision is a departure from the
terminology normally applied to Mars, i.e., referring to its peak layer as an F1 layer (Bougher et
al., 2001; Fox et al., 1995). That legacy came from the need to give a physical explanation for
the different altitudes of the Earth’s E and F1 layers. The very reasonable solution was to relate
them to the depths of penetration and ionization by solar radiation versus wavelength in the
terrestrial atmosphere (Rishbeth and Garriott, 1969; Bauer, 1973). In this way, the concept of an
ionospheric layer became a wavelength dependent phenomenon. Within the larger context of the
other planets (as well as comets and stars), we think a wavelength band-of-origin distinction
is a less transferable nomenclature than a distinction based on the dominance or not of
photochemistry.
2. THE EARTH’S IONOSPHERE: Variability Patterns
All of the ionospheric processes mentioned in Section 1 were discovered on Earth. The
observational database started with routine ionosonde measurements in 1931 (Rishbeth, 2001)
and, to a large extent, theory and simulations followed experimental and observational advances.
Among the terrestrial planets, Earth is the largest, its gravity is the strongest, and its
magnetosphere is unique. Its ionosphere spans an altitude range of ~60-2000 km, a significant
fraction of its radius (~30%), and the overall solar-terrestrial-interaction domain (“geospace”) is
measured in decades of earth radii.
There is a rich history of modeling the global morphologies of the Earth’s photochemical
ionospheric layers (e.g., Appleton (1959) to Titheridge (2003)). The same can be said for the F2layer physics that requires solution of the full continuity equation (production-loss-transport).
As reviewed recently by Forbes et al. (2000), Fuller-Rowell et al. (2000) and Rishbeth and
6
Mendillo (2001), the specification and modeling of the complex F2-layer patterns are well in
hand for time scales ranging from seasons to solar cycles. Understanding the variations during
episodic periods of geomagnetic activity and the day-to-day variability driven by coupling from
below are two main areas of current research in terrestrial aeronomy. As an illustration of dayto-day effects, we show in Figures 2 and 3 typical E, F1 and F2 layer peak densities and their
variabilities from ionosonde stations in Bermuda and Florida for the month of March 1999.
These sites were selected for this illustration because they are in the same longitude sector, and
their latitudes are well equatorward of any persistent influence of auroral zone processes; in
addition, they are sufficiently poleward to avoid variability effects caused by the
electrodynamics that forms the equatorial ionization anomaly (EIA) or “fountain effect” at low
latitudes. The top panels show the diurnal curves of NmF2 for the month, and the second panels
describe their variability (defined as the standard deviation about the mean). The corresponding
data for the NmF1 and NmE layers, and their variabilities, are in the lower four panels. Note that
nighttime densities in the E and F1 layers are too low to measure using standard ionosonde
techniques.
For the panels in Figures 2 and 3 containing the diurnal curves of NmF2, NmF1 and NmE, there is
an excellent consistency in their absolute values (giving virtually identical monthly mean
values), as would be expected for geographically similar stations. Of particular interest for this
study are the E and F1 patterns. The first thing to note is that the number of observations of an Elayer exceeds the number of detections of an F1-layer at the same location. This demonstrates
the problem of trying to monitor the F1-layer on a daily basis using an ionosonde. Yet, when
available, NmF1 values should be more or less in proportion to NmE, and this is indeed reflected
in their monthly mean values. According to the formulas in Rishbeth and Garriott (1969) which
give mean values for NmE and NmF1 as a function of sunspot number, their ratio should be ~2 for
the solar activity prevailing in March 1999, as this is the case in Figures 2 and 3. The situation is
rather different, however, for variabilities in each layer.
Consider first the variabilities for the F2 and E layers: the variability of ~20% (daytime) and 1540% (nighttime) for the F2-layer and ~5-7% (mid-day) for the E-layer are consistent at the two
sites separated by ~2100 km; their magnitudes are in agreement with many earlier studies. For
the F2-layer, it is well recognized that day-to-day variability of the ionosphere above any site
results from three independent sources: (1) solar photon variations, (2) magnetospheric activity,
and (3) coupling from the mesosphere-stratosphere-troposphere (collectively called “met” for
“meteorological”). In Rishbeth and Mendillo (2001), these were characterized as:
Σ2 (total) = Σ2 (solar) + Σ2 (geomag) + Σ2 (met)
(6)
For the daytime F-region, they were found to be ~3 %, 13%, and 15%, respectively, essentially
consistent with Forbes et al. (2000). Clearly, day-to-day changes in solar radiation exert a very
minor influence upon the F2-layer in comparison to those driven by dynamical effects imposed
from above and below.
For the E-layer, the day-to-day variations are much smaller than those in the F2-layer, and it is
reasonable to attribute them predominantly to photochemical effects (with perhaps some
contribution from tidal effects at the two sites). Titheridge (2000) found a ~6% variability for
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the E-layer, consistent with the earlier studies by Kouris and Muggleton (1973a, b), and certainly
with the patterns shown in the bottom panels of Figures 2 and 3.
For the F1-layer, however, the two stations do not show consistent variabilities. The mid-day
value at Eglin (Florida) is ~15%, nearly double that at Bermuda. Such a noticeable difference
between two nearby stations reinforces our concerns expressed earlier about using terrestrial F1layer analogies for Mars, and again for both observational and physical reasons. The visibility
and shape of the F1 ledge in ionosonde traces depend sensitively on the quantities α, β, and P
discussed above, which are affected by changes in neutral gas composition, and probably also by
geomagnetic activity and atmospheric waves. Relating F1-layer variabilities to solar input alone
cannot be done with any confidence. Thus, we conclude that the terrestrial E-layer data from
ionosondes is the appropriate source for comparative studies with the main photochemical layer
at Mars.
3. THE IONOSPHERE OF MARS
The planet Mars offers an interesting contrast to the terrestrial ionosphere. The Sun’s photon
flux is lower and, with no global magnetic field to shield it from the solar wind, heliospheric
particles and fields can also have a direct impact upon Mars’ upper atmosphere. While its
atmosphere at the surface is far thinner than Earth’s, the abundance of molecules near 130 km
(CO2 for Mars and N2 for Earth) are rather similar (~1011 cm-3). Photochemical equilibrium thus
controls the electron density at its peak height (hm ~135 km) and below. The scale height and
mean free path are comparable at 200 km, thus defining an exosphere relatively close to the peak
of the ionosphere. Moreover, the solar wind stand-off height (“ionopause”) is typically at 350
km, and thus magnetosphere-ionosphere interactions (so important on Earth) are replaced by
solar wind-ionosphere interactions at Mars. The total domain of ionospheric structures on Mars
thus spans a height range of only ~10% of its radius.
Two processes of coupling from below again distinguish Mars from Earth:
(1) the planet is small and yet its orographic features are dramatic, and thus tides and wave
forcing from below occur to a degree not seen on other terrestrial planets (Forbes and Hagan,
2000; Forbes, 2002);
(2) there are irregular crustal magnetic fields, predominantly in the southern hemisphere, that set
up mini-magnetospheric structures within its ionosphere, and thus solar wind coupling is
profoundly different in each hemisphere – a unique occurrence in the solar system.
A significant amount of work has been done by a community of modelers trying to understand
this complex ionosphere. In comparison to Earth, the ionosphere on Mars has been remarkably
under-sampled, and thus theory and modeling tend to be more advanced than the observational
database. The ionosphere-thermosphere problem has been studied in the framework of detailed
photochemistry (e.g., Fox et al., 1995), and with the use of global circulation models (GCMs) by
Bougher et al., (1991, 1999, 2000, 2002) and Winchester and Rees (1995). The first study of
coupling between lower and upper atmosphere GCMs has recently been described by (Bougher
et al., 2001). The solar wind’s interaction with the ionosphere has been studied within the joint
contexts of Venus and cometary plasma science (e.g., Shinagawa and Bougher, 1999; Kallio and
8
Janhunen, 2001; and Brecht, 1997, 2002), with a new model recently described by Ma et al.
(2003), that includes the effect of the crustal magnetic field.
Our results of a literature search for published electron density profiles on Mars are summarized
in Table 1. These discovery mode observations defined the initial phase of ionospheric studies at
Mars and provided the foundation material addressed by modelers. Taken as a group, the 433
electron density profiles have a broad coverage in latitude, local time and solar activity; they
have enabled basic comparative studies between Mars and Venus (e.g., Zhang et al., 1990a,b;
Kliore, 1992), and relationships to solar cycle activity (Hantsch and Bauer, 1990). In
comparison to Earth, however, where incoherent radars obtain complete Ne(h) profiles within
minutes, and ionosondes conduct routine monitoring at 15 minute intervals, the total Mars
database hardly exceeds a few days of terrestrial data at a single site. Of even greater concern is
that the spacing of missions over ~15 years profoundly limited the continuity in spatial and
temporal coverage, and thus comprehensive morphology patterns and their variability
characteristics have not been determined with confidence.
The prolonged period of unavailable ionospheric observations after Viking came to a dramatic
end in 1997 when the Mars Global Surveyor (MGS) satellite arrived at Mars. With a radio
science experiment to measure electron density profiles (Hinson et al., 1999), a plasma
instrument to determine solar wind and ionospheric boundaries (Mitchell et al., 2001), an
accelerometer to determine neutral atmospheric characteristics (Keating et al., 1998), and a
magnetometer that discovered crustal magnetic fields (Acuna et al., 1998), MGS created nothing
short of a re-birth of high altitude environmental science at Mars. In Section 4, we describe
briefly the use of radio occultation observations to derive electron density altitude profiles and
the levels of ionospheric variability they exhibit. In Section 5, we characterize terrestrial
ionospheric variability on the same days of the MGS results at Mars, and relate both to solar
irradiance patterns in Section 6, with summary and conclusions in Section 7.
4. THE MGS RADIO SCIENCE EXPERIMENT: Methods and Results.
4.1. Radio Occultation Techniques.
The MGS radio science (RS) experiment uses an onboard transmitter whose signal is received on
Earth as the satellite emerges from its orbit segments behind Mars. The signal is refracted
initially by high altitude plasma and then by the dense lower atmosphere. These “angle of
arrival” observations are then inverted to yield electron density profiles and neutral temperature
profiles, respectively. The geometrical properties of such limb-probing observations impose
limitations upon the local time coverage possible from occultation measurements (e.g., when
Mars is at opposition, most of the atmospheric samplings occur at periods near dawn and dusk).
These are times when solar illumination effects are changing rapidly at low latitudes, or
minimally at high latitudes, and thus not ideal cases for data-model comparisons. For the datasparse field of planetary ionospheres, these are nevertheless remarkable achievements.
For the MGS ionospheric retrievals, there are no a priori assumptions about the shape of the
electron density profile, or its peak density, but the electron density is assumed to be zero at
altitudes below 90 km. The standard deviation of the measurements varies among the
9
experiments, with a typical value of several thousand per cubic centimeter. Our interest is dayto-day variability, and thus we average two or more MGS profiles to reduce errors in the daily
mean profiles to approximately 2-3%. Further details of the MGS/RS experiment are given in
Hinson et al., (1999, 2001).
4.2. Case Studies.
MGS ionospheric profiles have been obtained for several periods since December 1998. The
Sun-Earth-Mars geometrical relationship for one of those periods (9-27 March 1999) is shown in
Figure 4. This period (with Mars near opposition) is clearly the best case for the study of
simultaneous solar effects upon Earth and Mars. For other orbital configurations, e.g., the
December 1998 data analyzed by Bougher et al. (2001), when the Sun-Earth-Mars angle was
~75° (Mars near quadrature), measurements of solar disk irradiance made at 1 AU would have to
be rotated by approximately 7 days, assuming constant solar active regions, to be appropriate for
illumination of Mars. The March 1999 period minimizes these concerns and hence is ideal for
comparative aeronomic analysis.
Figure 5(a) shows the 43 individual N(h) profiles obtained during the 19-day period in March
1999. Note that all profiles refer to a narrow range of latitudes (69.7°-73.3°N) and local times
(03:36-04:06). These profiles refer to different longitudes, as well as different days, on Mars
and, quite evidently, show considerable variability. Yet, there is a consistent peak with hm near
135 km and a secondary peak near 115 km. The altitude dependence of the standard deviation
about the sample mean is given in panel (b) and shows a ~10% variability at hm and ~15% for
the secondary peak at 115 km; topside variability increases with altitude.
To address variability among individual N(h) profiles, Bougher et al., (2001) analyzed a
somewhat smaller dataset comprised of the initial 32 N(h) profiles obtained over an 8-day period
(24 - 31 December 1998) with latitudes 64.7°-67.3°N and local times 03:18-04:18. The heights
of the maximum and secondary peak electron densities showed variations with longitude on
Mars, and a correlation analysis was conducted between those heights and the neutral
atmosphere density obtained from the accelerometer experiment. The results demonstrated a
linkage between wave-3 patterns in neutral density and the ionospheric heights. As discussed in
the context of equation (3), such vertical displacements of the thermosphere would not have a
first-order effect upon the peak electron densities since they occur near constant pressure levels.
That is, the ionospheric hm values could vary in absolute height units, but their electron densities
(Nm) would remain constant since the amount of penetrating ionizing radiation depends only on
the amount of overlying atmosphere.
Our interest in this study concerns day-to-day variability, and thus in Figure 5(c) we cast the 43
profiles into daily average values. Most of the 19 days had two to three profiles taken over a ~50
degree longitude range, and these were averaged to form the daily mean profiles. One day (10
March) had no MGS profiles and a second day (21 March) had only a single profile. Excluding
the latter led to 17 average daily N(h) profiles at a mean local time of 03:52. In panel (d), the
standard deviations about the 17-day mean are shown. Note that some of the variability from
panel (b) has been reduced by the daily/longitude averaging. The remaining variability (~5-7%
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at the main peak and ~10% at the secondary peak) thus represent our characterization of
ionospheric day-to-day variability on Mars for this period.
5. TERRESTRIAL IONOSPHERIC VARIABILITY DURING 9-27 MARCH 1999.
The MGS measurements described in Figure 5 pertain to the rather special conditions of summer
solstice at high latitudes, i.e., it is ~04 LT at ~71.5° N and the Sun is ~13 degrees above the
horizon (χ ~77°). On Earth, these days span an equinox period and thus “midnight sun”
conditions do not occur anywhere on the planet. In Antarctica, Zhongshan (69°S, 76°E) provides
the closest equivalent site for ionosonde measurements and, quite fortunately, data were taken on
all 17 days for which MGS observations are available at Mars. At 04 LT, the Sun is below the
horizon at Zhongshan, but at 8:30 LT, the solar zenith angle is ~77° (with a diurnal minimum at
noon of 68°), conditions favorable for comparison with the MGS results.
The diurnal patterns of the ionospheric layers above Zhongshan are shown in Figure 6.
Obviously there is considerable variability at this site. The lower panel showing the daily NmE
curves (formed from foE hourly values with 0.1 MHz resolution, as done in Figures 2 and 3)
shows a basic solar control of diurnal behavior. Yet, the standard deviations (Σ) for the daytime
period are rather large (~20%), and they increase as evening occurs (~40-65% from 18-20 LT).
The reason for this unusually high E-layer variability is the proximity of Zhongshan to the
auroral zone in the southern hemisphere. Thus, the “auroral-E” electron density enhancements
produced by precipitating magnetospheric particles dominate the day-to-day variability patterns
at most local times. This is most unfortunate from the perspective of comparative aeronomy, but
a nice reminder that ionospheric physics on Earth is a rich field of solar-terrestrial coupling.
In Figures 2 and 3, we showed the variability of the terrestrial E-, F1- and F2-layers above
Bermuda and Eglin (Florida), two “pure mid-latitude” sites. Since their E- and F2-layer
variabilities were consistent with many previous studies, we will return to those sites for our
initial assessment of ionospheric variability due to photochemical processes on Earth during 9-27
March 1999. Their 17-day means and associated variabilities during the MGS sample period
matched those of the full monthly datasets shown in Figures 2 and 3. To maximize diagnostic
accuracy for the photochemical E-layer, we will also abandon the requirement of matching the
low elevation angle of the MGS data, and simply examine the day-to-day variabilities for midday hours (11-13 LT). Using the mean of three hourly values also reduces the observational
errors in forming a daily value from ionosonde samplings with 0.1 MHz resolution to the same
levels associated with the MGS daily profiles (2-3%).
6. COMPARATIVE PHOTOCHEMICAL IONOSPHERES ON EARTH AND MARS.
6.1. Solar Variability in March 1999.
Having defined the terrestrial and martian datasets appropriate for comparative study, we now
turn to a description of the Sun’s variability during the period of interest. The solar energy flux
versus wavelength (called solar irradiance) that reached both planets each day between 9-27
March 1999 had to be virtually identical. Figure 7 shows several indices used to characterize
solar activity observed at 1 AU during that period. Quite fortunately, the emissions from the Sun
11
were not constant and thus Earth and Mars experienced the passage of a solar active region wellsuited for comparative aeronomic studies during a rather short period. The historical index to
gauge solar activity (the 10.7 cm solar radio flux, F10.7) varied from 103 units to 154 units, a
range comparable to the solar cycle's mean levels for a year of mid-to-low activity and a year of
moderate solar maximum, respectively.
The neutral atmospheres above terrestrial sites and at the MGS measurement point on Mars had
to respond in some way to such changes in solar input. The first-order effect of interest here,
however, is the photoionization of molecules spanning these days of solar variability, and thus
we will assume that any temporary changes in the neutral atmospheres are of secondary
importance to the values of peak electron density. To characterize the solar input for use in
equation (5), we will use the E10.7 curve in Figure 7. This index is used increasingly in
aeronomy to characterize the actual portion of the solar spectrum (EUV + X-rays) that accounts
for ionization of atmospheric constituents (see Tobiska et al., 2000, 2003). Thus, we will use
E10.7 as a proxy for the solar photon flux S at 1 AU in equation (5), and examine how it and the
other parameters of this equation compare at Earth and Mars. There are several types of
comparisons that can be made.
6.2. Comparison of Day-to-Day Photochemical Equilibrium on Earth and Mars.
As shown in equation (5), simple photochemical equilibrium within an invariant atmosphere at a
fixed distance from the Sun would result in a quadratic relationship between the maximum
electron density and the solar radiation responsible for ionization, i.e. Nm2~ S. To test this
relationship, we use the 17 daily values of Nm on Mars, NmE at Bermuda and at Eglin, averaged
over 11 – 13 LT, and the corresponding 17 values of the E10.7 indices to arrive at the results in
Figure 8. The best fit lines to the data are given by
(Nm(Mars))2
= 0.033 (E10.7) + 2.81 (109 e-/cm6)
(7)
(Nm(Earth))2 = 0.100 (E10.7) + 14.8 (109 e-/cm6)
(8)
In creating Figure 8, attention was given to the timing of the various measurements. For E10.7,
its component that depends on solar radio flux (F10.7) comes from observations made each day
at 17-23 UT (for a mean of 20 UT). At Bermuda and Eglin, noon conditions are at 16 and 18
UT, respectively, for a two-station mean of 17 UT. At Mars, the MGS observations each day
spanned 18-23 UT, and the “daily mean profiles” shown in Figure 5 had an average time of
20:54 UT. Thus, in all cases, the solar flux is determined prior to or close to the time of the
ionospheric observations on Mars and Earth. Figure 8 offers convincing evidence for solar
control of the photochemical ionospheric layers on Mars and Earth. If all photochemical species
and parameters were truly the same on both planets, the slopes of the lines in Figure 8 would
differ only by the square of their respective distances from the Sun. For Earth at 1 AU and Mars
at 1.52 AU, this amounts to a factor of 2.25. The empirical values shown in Figure 8 have a ratio
of about 3, implying that the assumptions leading to the use of equation (5) for scaling studies
are generally appropriate one. Finally, we note that while solar irradiance changes account for
the overall trend in Figure 8, there is still residual variability. It appears uncorrelated at the two
12
planets, and thus would likely be a combination of observational uncertainties and variabilities
causes by other processes unique to each planet.
While there are no independent dataset on Mars to confirm the MGS results for this month, there
are multiple sites on Earth available to confirm the terrestrial trend in Figure 8. While the global
ionosonde network is large, Bermuda and Eglin were selected because they alone had complete
coverage for 9-27 March 1999. Finding sites that were at comparable “pure midlatitudes”, but at
vastly different longitudes, and with more than 10 days of E-region data reported, proved rather
difficult. Useable data were available from Ahmedabad (India) and Hobart (Tasmania). Adding
those sites to the Bermuda, Florida and Antarctic sites already described, we show in Figure 9
correlation results for the E-layers at all five terrestrial locations examined in this study. The
patterns from Ahmedabad and Hobart, while not as complete as the results from the
Bermuda/Florida longitude sector, point to a reasonable confirmation of those trends in the
Asian sector and in the southern hemisphere. For Zhongshan, the auroral influence upon E-layer
variability clearly dominates. Most encouraging for the non-auroral sites is that the slopes
relating their Nm2 to E10.7 are all consistent at ~0.1.
6.3. Comparing Absolute Values of Electron Density at Earth and Mars.
Equation (5) can be recast to separate Nm and the purely geometrical factors from the
photochemical parameters, yielding,
Nm2 D2 sec χ
=
S η / α e H ~ constant
(9)
The left side of equation (9) involves known quantities, and thus one can readily test to see if
their product leads to a “constant” for the right hand term. This is done by taking the values of
Nm2 (in units of 109 cm-6) at E10.7 = 125 units for Earth and Mars from Figure 8, and noting that
for equinox conditions χ ~ latitude (which is 31o for the mean of Bermuda and Eglin), while for
Mars χ = 77û; D = 1 for Earth and 1.5 for Mars. The computed value of Nm2D2 sec χ at Mars (69)
is about twice the terrestrial value (32). At our present level of investigation, agreement of
squared quantities to within a factor of 2 seems quite satisfactory. It implies that all the Nm
values at Mars are ~ 40% larger than anticipated from the simplifying set of assumptions that led
to equation (9). Considering the array of physical parameters on the right hand side that also
form the constant, a factor of two difference in their product is reasonable. Differences will
occur in the spectral range for S and the ionization efficiencies η leading to the production of O2+
at each planet, as will the appropriate scale height H to use at each planet. As shown in Bougher
et al. (2002), H can vary in the 5-10 km range at both planets for the altitudes of interest here.
Our computations show that the main uncertainty in H is due to rapidly changing temperatures
with altitude, a far more important trend on Earth than on Mars. In Chapman theory, this enters
as a modification to the exponent of the sec χ term in equation (9). Titheridge (2000) shows this
factor to be 1.2-1.3 under most conditions at Earth; using MSIS for March 1999 we find it
somewhat larger (1.4). This correction would be appropriate only for the terrestrial constant, and
it only reduces the factor of 2 differences by about 10%. A larger effect would result from the
ionization frequencies for CO2 and O2, defined as J, the ionization rate per unit neutral gas
molecule at the top of the atmosphere, i.e., <Sσ> averaged over wavelength. As shown in Table
13
9.2 in Schunk and Nagy (2000), the J-value for CO2 is larger than for O2 at 1 AU, making the S η
proxy in equation (4) the dominant source of difference between Earth and Mars.
6.4. Comparing Earth and Mars Ionospheres at Constant Solar Zenith Angle.
Returning to equation (5), there is one final scaling test to be made, namely the Nm ~1/D relation
for identical latitude and solar zenith angle conditions at the two planets. The only terrestrial site
where this is possible is Zhongshan, where average conditions in the E-layer should reflect solar
production (but not its variability, as discussed above). The Zhongshan monthly mean at 77o (at
08:30 LT in Figure 6) is 7 × 104 e-/cm3 which, when scaled down by D = 1.52, gives 4.6 ×104 e/cm3 for the Martian ionosphere. The observed mean value from MGS in Figure 5 is 8 ×104 e/cm3 which would have to be reduced by 40%, in agreement with the estimate made in Section
6.3 using equation (9).
7. CONCLUSIONS
This first attempt to relate ionospheric variability on two planets results from the recent
availability of consecutive day observations of the electron density profiles from the Mars Global
Surveyor (MGS) satellite during a period when Mars and Earth were nearly aligned with the Sun.
The MGS daily peak electron densities were analyzed in conjunction with daily values of the
terrestrial E-layer’s peak density and a daily solar index for production. A unified
photochemical equilibrium explanation for the trends seen on both planets has been obtained.
The period sampled did not include episodes of enhanced geomagnetic activity, and the MGS
profiles did not show evidence for a compressed ionopause location, and thus solar wind induced
perturbations (that might have an influence via downward coupling to photochemical layers)
could not be addressed and remain as an open, interesting issue. While solar flux changes alone
were sufficient to account for the basic trends in observed variabilities, residuals do remain.
These are uncorrelated and appear to be larger at Mars. Different types of upward coupling from
neutral atmosphere dynamics are perhaps the major unknown sources of quiet-time variability at
both planets. Detailed modeling of this period using a constant neutral atmosphere and 17 daily
irradiance spectra has been conducted by Martinis et al. (2003), and values of ±5-10% variability
are easily accounted for by solar effects alone. Finally, the MGS dataset is extensive and future
observational periods to be analyzed may well contain evidence for solar wind impact effects
upon the ionospheric profiles. This would expand current notions of “space weather”
ionospheric variability on Earth to a more general case of solar/terrestrial-planet space weather.
Acknowledgements. Ionosonde data used in this study were provided by the World Data Center
in Boulder, CO. Support for this work at Boston University was provided by the NASA MGS
Data Analysis grants program, and by seed research funds from the Center for Space Physics.
We are grateful to Luke Moore for assistance in the data analysis, and Carlos Martinis for useful
discussions. Funding for work at Stanford University was provided by the Mars Global
Surveyor Project.
14
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17
Table 1. Summary of Ionospheric Measurements at Mars Prior to the Mars Global
Surveyor Mission
Mission
Mariner 4a
Mariner 6d
Mariner 7d
Mars 2ck
Mariner 9e
Ext. Mission 1g
Ext. Mission 2gh
Mars 4cklm
Mars 5l
Mars 6ckm
Viking 1b
ij
Viking 2b
ij
Type
FN
FX
FN
FX
FN
FX
ON/X
ON
OX
ON
OX
ON/X
FN
FX
OX
FN
Lander
ON/X
Lander
ON/X
Dates
14 Jun 1965
14 Jun 1965
31 Jul 1969
31 Jul 1969
5 Aug 1969
5 Aug 1969
Nov-Dec 1971
14 Nov-23 Dec 71
14 Nov-23 Dec 71
7 May-25 Jun 72
7 May-25 Jun 72
29 Sep-26 Oct 72
10 Feb 1974
10 Feb 1974
18 Feb 1974
3 Mar 1974
20 Jul 1976
20 Jul 76-17 Aug 80
3 Sep 1976
3 Sep 76-25 Jul 78
#N(h)
1
1#
1
1
1
1
4
76
78
39
25
44
1
1
1
1
1
113*
1
42*
SZA
67
~115
57
107
56
130
~50
47-56
57-105
70-80
95-115
88-100
82
127
106
72
44-37
50-125
45-53
80-112
Lat.
50S
60N
4N
79N
58N
38N
9N-12N
40S-30N
34N-65N
40S-86N
80S-5N
65S-55S
52S
9S@
38N
35S
17N-9N
74S-69N
42N-34N
67S-73N
Long.
LT
177E
13:00
36W
23:40
356E
15:34
87E
22:10
30E
14:30
212E
03:10
23-360E 09-16+
all
17-14
all
17-14
60-330E 18-06
all
05-18
all
09-13
17W
07:42+
236W
03:30
214W
04:30
14W
19:33+
56-66W
16:13
all
03-20
236-246W 09:49
all
04-21
Key:
F: fly-by, O: orbiter; N: ingress, X: egress; #Poor data; *From 1.88 years (1 Mars year); + ±2 hours; @Given as 90 S in ref l.
#N(h) is the number of electron density profiles, SZA is solar zenith angle.
Footnotes :
a
e
j
b
g
k
Fjeldbo, et al., 1966.
Hanson, et al., 1977.
c
Kolosov, et al., , 1975.
d
Kliore, et al, 1971.
Kliore, et al., 1972.
Kliore, et al., 1973.
h
Kliore, 1974.
i
Kliore, 1992.
Lindal, et al., 1979.
Moroz, 1976.
l
Savich, and Samovol, 1976.
m
Vasilyev, et al., 1975.
18
Figure 1. A summary of ionospheric characteristics in the solar system. The solid triangles and vertical
lines give typical values and ranges of the maximum electron density for the photochemical ionospheric
layers at the seven planets with permanent and substantial atmospheres. For Earth, two values are given,
an open triangle for the F2-layer and a solid triangle for daytime E-layer. A best fit curve to the seven
solid triangles using the dependence shown in equation (5) is given. See text for discussion.
19
Figure 2. Examples of terrestrial ionospheric variability at a midlatitude site (Bermuda, 32°N, 64°W).
Top panels give F2-layer diurnal curves of NmF2 and their variability (Σ), defined as the standard
deviation (in percent) about the monthly mean. Lower panels give simultaneous diurnal patterns for the
F1-and E-layer peak densities and their variabilities.
20
Figure 3. Same as in Figure 2, but for ionosonde data from Eglin, Florida (30oN, 86oW).
21
Figure 4. Geometry of Sun, Earth and Mars during the 19-day period 9-27 March 1999. The solid dots
give the position of Earth and Mars on the 9th and the thin solid lines their positions on the 27th.
22
Figure 5. Electron density profiles from the Mars Global Surveyor (MGS) radio science experiment for 9-27
March 1999. All measurements refer to latitudes in the range 69.7°-73.3°N and 26.5°-273.0°W on Mars. The local
times sampled were 3.6-4.1 hours, and the solar zenith angles were 76.5°-77.8°. Panel (a) gives the 43 individual
profiles obtained (1 to 3 per day distributed in longitude) and panel (b) the standard deviation about the sample
mean. Panel (c) gives longitude-averaged profiles for each day containing two or more profiles from (a), and panel
(d) portrays the daily variability about that sample’s mean.
23
Figure 6. Ionosonde data from the PRC’s Zhongshan station in Antarctica (69°S, 76°E) for March 1999,
using the same format as in Figures 2 and 3. Note that the variabilities (Σ) at this auroral zone station are
larger than those at the midlatitude stations in Figure 2 and 3.
24
Figure 7. Three indices that portray solar activity during the period of MGS data at Mars: Lyman-α
emission, F10.7 radio flux and the new E10.7 index that combines several diagnostics of solar activity for
use in aeronomic studies (Tobiska, 2000).
25
Figure 8. Comparisons of Nm on Mars and same-day values of NmE on Earth with the corresponding E10.7 daily
indices for 17 days within the period 9-27 March 1999. Daytime hourly values (11-13 LT) were averaged from the
Bermuda and Eglin ionosonde sites to form the terrestrial daily values with experimental uncertainties approximately
equal to those for the MGS daily means (2-3%). For correlations within the framework of photochemical equilibrium,
the square of the electron density is related to solar flux by a linear fit (see text).
26
Figure 9. Comparisons of terrestrial NmE patterns vs solar flux using the same format as in Figure 8 for the 17 day
MGS period in March 1999. In addition to the Bermuda and Elgin sites used to create Figure 8, the ionosonde
station at Ahmedabad (India, 23°N, 72°E), was selected because of its very different longitude, and the station in
Hobart (Tasmania, Australia, 43°S, 147°E), provides mid-latitude coverage from the southern hemisphere.
Bermuda and Elgin each have full coverage for the 17 days of MGS data during 9-27 March 1999, Ahmedabad had
10 days and Hobart 12 days. The lowest panels give results from the Antarctic auroral zone station Zhongshan,
using data from Figure 6.
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